1. Field of the Invention
The disclosure relates to a transmitting device, a receiving device, and a transmitting and receiving system, which enable accurate decompression even if the original input digital signal has low sparsity.
2. Related Art
In wireless sensor nodes, for which low power consumption is demanded, reducing the wireless transmission power, which largely accounts for the power consumption, is indispensable. One of techniques therefor is reducing the wireless transmission power by reducing the amount of data by data compression of transmission data.
In general data compression, compression techniques, such as of ZIP and LZH, are often used. Data compression by these compression techniques requires many arithmetic operations, and thus is not suitable for implementation on wireless sensor nodes, for which low power consumption is demanded. For example, if such data compression is applied to a wireless sensor node, power consumed by compression operations may become greater than the amount of reduction in the wireless transmission power and the overall power consumption may actually be increased.
Compressive sensing is a technique that allows data compression with low power consumption. Compressive sensing is described in detail in, for example, “Implementation of Compressive Sensing on Sensor Node by Use of Circulation Matrix and Evaluation of Power Consumption”, by Tatsuya Sasaki, IPSJ SIG Technical Report 2012 (hereinafter, referred to as Sasaki document). Briefly stated, this compressive sensing is a technique for accurately executing decompression into the original signal, from data that have been compressed to a small number of data, by utilizing signal sparsity, which many signals in nature are said to have. In compressive sensing, since compression operations are executed with matrix products only, the operations are easy, and in particular, in the Sasaki document, by using, as a matrix used in the arithmetic operation, a random observation matrix, in which ±1 is randomly arranged as the elements, compression operations are realized by addition and subtraction only.
Specifically, if the number of original data is N, and the number of data that have been compressed as a result of compression operations is M, N>M is satisfied, naturally. If the original data are represented by an input digital signal x, which is an N-dimensional vector, and the data after compression are represented by a compressed digital signal d, which is an M-dimensional vector, by compression operations in compressive sensing, as expressed by the following Equation (1), the compressed digital signal d is able to be found by multiplying the input digital signal x by an observation matrix Φ of M rows and N columns.d=Φx  (1)The original input digital signal x needs to have sparsity. When the input digital signal x has sparsity, the input digital signal x is expressed by the following Equation (2) by use of an appropriate basis transformation matrix Ψ of N rows and N columns.x=Ψs  (2)When s is an N-dimensional vector and the input digital signal x has sparsity, most of the vector components of s become 0.
If a matrix having random elements is used as the observation matrix Φ when the input digital signal x has the above mentioned sparsity, based on the observation matrix Φ, the basis transformation matrix Ψ, and the compressed digital signal d, by use of L1-norm minimization or the like, the original input digital signal x is able to be accurately decompressed.
In the Sasaki document, by using, as the observation matrix Φ, the matrix with randomly arranged ±1, compression operations are realized by addition and subtraction only. Further, the amount of arithmetic operations upon data compression is M×N since Equation (1) represents matrix product operation.
Further, in Japanese Patent Application Publication No. 2013-90097, a technique, for reducing the amount of arithmetic operations upon data compression from M×N to N+N×(log 2)N, by use of FFT, is disclosed.